Poe's Poet-Mathematician: Evariste Galois

III. Where Does Science Come From? Poe’s Poet-Mathematician: Evariste Galois by David Shavin

Poe’s Dupin: “As poet and determined from the overall di- mathematician, he would rection discovered by the geo- reason well; as mere mathe- metric overview. It was this matician, he could not have grand manner of considering the reasoned at all.” shapes of nature, which was dis- Poe’s Narrator to Dupin: covered by the students of “You have a quarrel on hand, Monge . . .”1 I see,” said I, “with some of the algebraists of Paris . . .” I. Dupin, Poe’s Poet- Mathematician Charles Dupin (1819) on Descriptive Geometry Aug. 20—In 1841, Edgar Allan On the “general and purely Poe created the fictional charac- rational geometry, of which de- ter, the poet mathematician C. scriptive geometry is only the Auguste Dupin. He first appears graphic translation . . . one’s in “The Murders in the Rue mind must be especially trained Morgue” (MRM), in which his in this general geometry. One “descriptive geometry” method must be able to represent the succeeds in solving the crime, shapes of bodies in space, and to Evariste Galois while the detailed and exhaus- ideally combine these shapes by tive methods of Police Prefect the sole power of imagination. The mind learns to see G____ prove hopeless. In the previous year, 1840, Pre- inwardly and with perfect clarity the individual lines fect G____, that is, the Police Prefect of Paris, Henri and surfaces, and families of lines and surfaces; it ac- Louis Gisquet, had issued his Memoires, which in- quires a feeling for the character of these families and cluded a curious dismissal of the violent death of Eva- individuals; it learns to see them, combine them, and riste Galois, one of the poet-mathematician students of foresee the results of their intersections and of their Gauss’ epic, Disquisitiones Arithmeticae.2 The case is more or less intimate contacts, etc. Thus the new geom- made here that Poe’s poet-mathematician, in real life, etry greatly strengthens the imagination; it teaches you was Galois, and further, that Poe’s Dupin would secure how to grasp a vast collection of shapes quickly and justice for Galois. precisely, to judge their similarities and differences and their relations of size and position . . .” For example, re- 1. Charles Dupin, 1819, “Historical Essay on the Contributions and garding designing roads or railways through the coun- Scientific Works of Gaspard Monge,” translated by Larry Hecht. tryside, “. . . engineering drawings are needed only for 2. “The Generation of ‘Poet-Mathematicians’: The Case of Niels limited areas in which the best route to follow is easily Abel,” by David Shavin, EIR, Vol. 44, Issue 30, July 28, 2017.

September 1, 2017 EIR Wake Up Call from Houston 47 First, we look at Poe’s characterization of the particular genius of Dupin. In MRM, the first of Poe’s three “Dupin” tales, Poe challenges the reader with his Narrator’s (N’s) description of Dupin’s unique method of analysis. After walking together in silence for a quarter-hour, Dupin casu- ally reads N’s mind with a line that seems to come from nowhere—that the actor Chantilly is indeed too short for the role of “Xerxes.” N is dumbstruck. By what power had Dupin divined N’s private thoughts? Dupin explains his chain of reasoning: A stranger had bumped N, causing a brush with a pile of paving stones and discomfort to his ankle. A bit later on, upon encounter- ing some advanced street paving, with “overlapping and riveted blocks,” Dupin noticed that N’s face brightened, and N murmured the word, “stereotomy.” (So, illustration by Frédéric Théodore Lix the art of three-dimensional cutting and C. Auguste Dupin, illustration for The Puloined Letter by Edgar Allan Poe. fashioning—an element of descriptive geometry—can improve life, helping to avoid injuries Only then had Dupin dared to articulate: “He is a very from more backward alleyways.) The two of them had little fellow, that’s true, and would do better for the The- shared discussions on stereotomy, so the matter of the atres des Varietes.” properties of constituent parts being developed from What should one make of a power to trace causal the characteristics of the larger dimensionality was a moves of the imagination and of the mind, combined shared thought process. From their recent discussions with a few selected empirical confirmations? Before about both Epicurus and “atomies,” or how the proper- dismissing Dupin’s bold reasoning, consider N’s reflec- ties of the very small come about, the next part of their tion: “There are few persons who have not, at some recent discussions was suggested. period of their lives, amused themselves in retracing the This was, how the ancient Epicurus’ conjectures steps by which particular conclusions of their own were in line with recent astronomical developments, minds have been attained. The occupation is often full that of the nebular cosmogony and the nebula of Orion! of interest; and he who attempts it for the first time is (Poe refers to a Dr. Nichol, a popularizer of John Her- astonished by the apparently illimitable goal.” Is there schel’s work on the organization, beyond the solar any child whose imagination has led him or her, per- system, of galaxies.)3 When N next turned to look up at haps at night before falling asleep, down strange ave- the stars, Dupin felt confirmed in his reasonings. Dupin nues—and who, occasionally, hasn’t asked himself reminded N that they had both read and discussed, in how he arrived at that point in his internal dialogue? the previous day’s newspaper, a reference to Orion, There is a marvelous power to be acquired, though with which was included as part of an attack upon the actor no little difficulty, in training oneself, after allowing the Chantilly. When N smiled and altered his “stooping” imagination to roam, to then retrace the steps, working posture, drawing himself up to full height, Dupin knew backwards. One learns secrets about oneself and, also, that N made the connection from Orion to the diminu- one develops the power of mind, of analysis. Poe’s tive Chantilly playing roles that were too big for him. boldness is that he openly, audaciously, addresses the development of that power.

3. Dr. J.P. Nichol’s 1838 Views of the Architecture of the Heavens fea- In 1842, Poe’s Dupin character reappears in “The tured an engraved plate from Herschel’s telescope, both shocking and Mystery of Marie Roget,” based upon an actual, un- charming the public with a representation of our Milky Way galaxy. solved murder case in New York City. Dupin is further

48 Wake Up Call from Houston EIR September 1, 2017 developed in “The Purloined Letter” (1844). There, a “But is this really the poet?” I asked. “There are crafty minister in the French government has stolen a two brothers, I know; and both have attained reputation document that compromises the Queen, and proceeds in letters. The Minister I believe has written learnedly to blackmail her over policy matters. The minister is on the Differential Calculus. He is a mathematician, waylaid and searched more than once by Gisquet’s and no poet.” minions, to rule out his carrying the document on his “You are mistaken; I know him well; he is both. As person. It is known that the document is in the minis- poet and mathematician, he would reason well; as mere ter’s apartments, a finite area that Gisquet has searched mathematician, he could not have reasoned at all, and inch by inch in excruciating detail. Dupin tells Gisquet thus would have been at the mercy of the Prefect.” that the minister “. . . is not altogether a fool, and, if not, “You surprise me,” I said, “by these opinions, which must have anticipated these waylayings, as a matter of have been contradicted by the voice of the world. You course.” “Not altogether a fool,” said Gisquet, “but then do not mean to set at naught the well-digested idea of he’s a poet, which I take to be only one remove from a centuries. The mathematical reason has long been re- fool.” “True,” said Dupin, “. . . although I have been garded as the reason par excellence.” guilty of certain doggerel myself.” Dupin proceeds to “. . . The mathematicians, I grant you, have done discover the document almost immediately, astonish- their best to promulgate the popular error to which you ing N; and he does so, based primarily upon his analysis allude, and which is none the less an error for its prom- of the minister’s mind. He explains Gisquet’s short- ulgation as truth . . . [Further, T]hey have insinuated the coming: term ‘analysis’ into application to algebra. The French “This functionary, however, has been thoroughly are the originators of this particular deception. . . .” mystified; and the remote source of his defeat lies in the “You have a quarrel on hand, I see,” said I, “with supposition that the Minister is a fool, because he has some of the algebraists of Paris . . .” acquired renown as a poet. All fools are poets; this the “The great error lies in supposing that even the Prefect feels, and he is merely guilty . . . in thence infer- truths of what is called pure algebra, are abstract or ring that all poets are fools.” general truths.”

with the disorder of the whole structure. It would seem that the ideas are so precious to the author that Poe and Galois he abhors the pain of connecting them with each Compare Poe and Galois. Poe’s 1844: “. . . The other, while at the same time his mind is so exhausted mathematicians, I grant you, have done their best to by the concepts which form the foundations of his promulgate the popular error to which you allude, work that he cannot produce one single thought that and which is none the less an error for its promulga- would coordinate this ensemble. Sometimes you tion as truth . . . [Further, T]hey have insinuated the seem to encounter a method, a connection, a coordi- term ‘analysis’ into application to algebra. The nation. But all this is wrong and artificial. You will French are the originators of this particular decep- find divisions of material for which there is no reason, tion. . . .” In January 1831, the revolutionary 19-year- arbitrary connections, conventional arrangements. old, Galois, gave a series of classes in a Paris book- These faults, still more glaring than the absence of all store for the youth of Paris. His introduction: “Of all method, you will find chiefly in books written by human knowledge, we know that mathematics is the men who do not know what they are writing about. most abstract, the most logical, the only one which All this must seem especially astonishing to people does not appeal to the world of our sense impres- for whom the word ‘mathematics’ is synonymous sions. Often one concludes that mathematics is, on with ‘rigor.’ ” the whole, the most methodic, the most coordinated This is Infeld’s translation of Galois’ notes. It branch of science. But this is an error. seems to be his reconstruction of the opening of the “Take any book on algebra, whether a textbook or lecture series. He notes: “The lecture given in Cail- an original work, and you will see in it a confused lot’s bookshop is genuine Galois; it is based on one mass of propositions, whose rigor contrasts strangely of Galois’ notes in his posthumous papers.”

September 1, 2017 EIR Wake Up Call from Houston 49 II. A Quarrel with the Algebraists of attempted coverup of Galois’ death that Poe would of Paris have recognized immediately. It made for a case worthy of Dupin’s analytic abilities. Poe concludes his “Mur- Evariste Galois was the genius who, more than ders in the Rue Morgue” with Dupin’s skewering of anyone else of the time, developed Gauss’ approach to Police Prefect Gisquet: “I like him especially for one the underlying laws of “pure algebra.” Galois’ method master stroke of cant, by which he has attained his repu- revived the physical geometry approach of the five Pla- tation for ingenuity. I mean the way he has ‘of denying tonic solids and of Kepler, as transmitted through what is, and explaining what isn’t.’ ” Gisquet’s explana- Gauss.4 Of this, more below. It was the chief algebraist tion of Galois’ death: A friend killed him. of Paris, Augustin-Louis Cauchy, who did all he could to bury Galois’ manuscript. It was Cauchy’s factional allies who did all they could to bury Galois. Poe, a III. ‘What Is’—The Genius of decade later, found the matter worth reviving. Galois Now for a brief introduction of two leading characters. Cauchy was a loyal administrator for the Restora- Both Cauchy and Gisquet did their best to deny tion monarchs, Louis XVIII and Charles X, imposed what is—that Galois was a genius. First, a quick char- upon France, 1815 to 1830, in the wake of the Congress acterization of Galois’ approach. of Vienna. In 1815, Gaspard Monge and Lazare Carnot Galois had just turned fifteen, in the Paris of 1826, were thrown out of their republican Ecole Polytech- when Abel’s method for analyzing higher-powered nique, and Cauchy was installed as overseer. In two in- equations was announced to the French Academy. Be- famous and thuggish cases, Cauchy accepted scientific tween 1823 and 1829, Dirichlet, Abel, and then treatises, under the obligation of making a report on Galois—all based on Gauss’ work—had treated the cu- them to the Academy of Sciences, and instead, he buried rious situation in which equations up to the fourth them. In 1826, Cauchy had buried Niels Abel’s scien- power could be submitted to algorithms, but beginning tific treatise and, despite the hazard of a second such with the fifth power, the “quintic,” nature seemed to extraordinary “accident,” he was not embarrassed to defy such treatment. Even though Cauchy had buried repeat this performance in 1829 with Galois’ first two Abel’s paper (and Abel had died a month or two before submissions—and very likely, even Galois’ third sub- Galois’ first two papers were presented to the French mission in 1830. (Four unlikely accidents occurring Academy), Galois had effectively succeeded in extend- one after the other—but if anyone could calculate the ing Abel’s approach to the quintic, and to solving odds of that occurring, Cauchy could!) When Charles X higher-powered equations in general. In so doing, he abdicated in July 1830, Cauchy left France, leaving his developed a higher-powered language to examine what family behind. He would spend five years trying to tutor was going on. Imagine Cauchy’s frustration in June an unwilling teenager, the grandson of Charles X and 1829, when he realized his earlier, thuggish action his chosen heir to the throne, as part of their plan to re- might be to no avail. conquer France. Galois developed an analysis of equations based Henri-Joseph Gisquet, Police Prefect in Paris from upon the symmetries, and non-symmetries, of the five 1831 to 1836, was likely the man most responsible for Platonic solids. An equation could be factored, could be the death, at age 20, of Evariste Galois. He certainly led broken into constituent parts, if symmetries, or even the suppression of Galois’ political movement. Poe’s partial symmetries, could be located. If no symmetries MRM tale identifies Gisquet’s methods with those of an were locatable, the equation could not be factored. earlier prefect, Vidocq, and Poe would have been famil- (These symmetries are typically explained by delving iar with at least parts of both of their memoirs.5 Gis- into the symmetries in the representation of the coeffi- quet’s own memoir, published in 1840, the year prior to cients, or characteristics of a formula, by matrices. the appearance of C. Auguste Dupin, included the type However, the fascination with bookkeeping matters there, tends to obscure the principle.) A simple case of this type of analysis is reflected in the exercise students 4. For example, compare the bulk of Gauss’s 1799 “Fundamental The- orem of Algebra” with his drawing at the end. go through in determining whether a number is com- 5. Portions of Vidocq’s memoirs appeared in Burton’s Magazine, 1838- posite or prime—the factors are primitive “subgroups” 1839. Poe was an editor of Burton’s in 1839-1840. of a number.

50 Wake Up Call from Houston EIR September 1, 2017 A somewhat more complicated case arises with among equals,” the dodecahedron—whence the other Gauss’ analysis, where some bases revolve through a four are best situated).6 Galois developed that new lan- given modulus without ever repeating until all possible guage, involving what are called modular functions. residues are given, while others form subgroups of re- When confronted with an apparent barrier at the fifth peated patterns before they ever cover all the possible power, Galois took Abel’s hint that we would not residues. The powers of three—3, 9, 27, 81, etc.—are solve—and properly benefit from—this barrier by any expressed in a modulus-5 system as 3, 4, 2, 1. (These normal extension of the methods developed from 2nd, are what is “left over,” the residue, after the modulus of 3rd, and 4th power solutions. And he took the Creator’s five is divided into the number.) These four “residues” hint, just as in Plato’s Timaeus dialogue, that man is will keep repeating, and they cover all the possibilities fulfilling his historical mission if he pursues the myste- in a modulus-5 world. However, the powers of four—4, rious and rather miraculous, unseen powers that are 16, 64, 256, etc.—become 4, 1, 4, 1, etc. Four, in modulus-5, forms a subgroup that does not exhaust all the 6. Unfortunately, the closest most students get to even a hint of such possibilities. In the modulus-5 world, 3 acts, loosely symmetries is in the expansion of a sum raised to a power. They are told speaking, more “prime”-like than the more “composite”- to use Pascal’s Triangle, in which the same coefficient appears sym- like 4. metrically. (That is, for a fifth power expansion, having six terms, they The power of mind had to be developed to “see” the pair up as 1st and 6th, the 2nd and 5th, and the 3rd and 4th.) However, even this simple symmetrical character is left unaddressed and unex- rich interplay amongst the five Platonic solids (the plained. Instead, the student gets the practical advice: “Learn the rule. It cube, tetrahedron, octahedron, icosahedron, and “first works.”

Klein problem as such: “Those choices of starting points set the stage for Klein’s crucial, false assump- From Galois to tion, set forth on pp. 58-59 [of Klein’s Famous Prob- lems]: ‘The period from 1670 to 1770, characterized ‘Group Theory’ by the names of Leibniz, Newton, and Euler, saw the Felix Klein, in his Lectures on the Icosahedrons rise of modern analysis. Great discoveries followed and the Solution of Equations of the Fifth Degree, one another in such an almost unbroken series that, would give permission to mathematicians to neutral- as was natural, critical rigor fell into the background. ize the Platonic solids, treating them as merely a rep- For our purposes the development of the theory of resentation equivalent to the matrices. But there is a series is especially important.’ With that silly bit of difference between the foot and the footprint. As a pedagogical hand waving there, you have Klein’s result, Galois’ employment of the word groupe has hoax set into place on stage. Henceforth, everything become the label for a group theory in which most said by Klein is an extension of that whopper, that “group theoreticians” end up playing with the num- fallacy of composition. bers with little or no idea of the “descriptive geome- “The crucial code words from that citation are try” approach rooted in the Platonic solids. (A re- ‘analysis’ and infinite ‘series’. Those code words’ lated, but simpler, illustration of this is involved in appearance rightly implies that Klein is not address- the preference for digital computation over analogue ing the ontological problem of species distinction, computers.) Klein’s problem originated in the mis- which he only pretends to be attacking; he is engaged take that we had Poe’s Dupin cite earlier, “they have in a sleight of hand, pretending to address an onto- insinuated the term ‘analysis’ into application to al- logical problem, while considering only a formal gebra. The French are the originators of this particu- one. He is addressing a problem in infinite series; he lar deception. . . .” is using the credibility of Hermite’s and Lindemann’s Leibniz’s “analysis situs” is neutered and assimi- work on this problem of infinite series, to deflect the lated into previous algebraic techniques. See Lyndon viewer’s attention from the fact that he is not ad- LaRouche, in his “How Bertrand Russell Became an dressing the ontological problem at all. That is the Evil Man” (Fidelio, Fall 1984), who identified the formal nature of his fraud.”

September 1, 2017 EIR Wake Up Call from Houston 51 found to shape and structure the world as presented to us. Again, Charles Dupin’s discussion of “descriptive geometry,” ten years prior to Galois’ paper, appears as an excellent estimate of Galois’ process: “One must be able to represent the shapes of bodies in space, and to ideally combine these shapes by the sole power of imagination. The mind learns to see inwardly and with perfect clarity the individual lines and surfaces, and families of lines and surfaces; it acquires a feeling for the character of these families and individuals; it learns to see them combine them, and foresee the results of their intersections and of their more or less intimate contacts, etc. Thus the new geometry greatly strengthens the imagination; it teaches you how to grasp a vast collection of shapes quickly and precisely, to judge their similarities and differences and their relations of size and position. . . .”

IV. Galois, Revolutionary- Mathematician

Poe has the Narrator in “The Purloined Letter” address Dupin: “ ‘You have a quarrel Niels Abel’s manuscript that was buried by Cauchy. on hand, I see,’ said I, ‘with some of the algebraists of Paris . . .’ ” Galois was the outstanding exam- vousness at the Academy over Cauchy’s heavy-handed ple of Dupin’s quarrel with the algebraists of Paris. We tactics, for Legendre seems to have manufactured a wish to deal with Galois’ last year, before his death at cover story for Cauchy. He pretended to Jacobi that he age 20, as a prisoner of Police Prefect Gisquet. For that and Cauchy had agreed to ask Abel for a neater copy, purpose, let’s fill in Galois’ story with a summary of his since “we perceived that the memoir was barely legible; tumultuous last three years, beginning with his first it was written in ink almost white, the letters badly submission to the French Academy of Sciences. formed . . .” However, when the document was finally dug out of the Academy in 1840, it was quite legible— Cauchy Buries Galois’ Paper remaining so even today.7 Clearly, something was cloud- Galois, still five months shy of eighteen, submitted ing the “perceptions” in Paris, and there is no reason to two papers to the Academy of Sciences on May 25 and believe Abel was at fault for failing to provide a “neater June 1, 1829. Cauchy took possession of them, as he copy.” Jacobi’s 1829 inquiry, in bringing attention to was to make the report on them to the Academy. Then on Cauchy’s previous fraud, would normally have been June 22, 1829, the news of the April 7 death of Niels enough for most ideologues to give pause before claim- Abel was announced at the French Academy. At the ing a second misplacing of a submitted paper.8 time, Cauchy had held Abel’s memoire for three years, and Galois’ for only three weeks. Karl Jacobi, the col- 7. Legendre’s evasion suggests that he estimated Cauchy’s intent, as of the Spring of 1829, that the document would never see the light of day. laborator of both Abel and Lejeune Dirichlet, brought Otherwise, he likely would not have ventured such a cover. attention to Cauchy’s malfeasance, and attempted to get 8. Abel’s manuscript was not produced until 1840, upon official diplo- Abel’s manuscript from Cauchy. There was evident ner- matic pressure of the Norwegian consul.

52 Wake Up Call from Houston EIR September 1, 2017 At this same time that Galois was launching his scientific career, his father died under bizarre circum- stances. Nicholas-Gabriel Galois, the popular and witty mayor of a small town near Paris for the previous fifteen years, was targeted for destruc- tion by the town’s new Jesuit priest, who had allied himself with some Ultramontanists, local en- emies of the mayor. They manufactured a scandal by circulating vulgar epi- grams directed against locals, and forging the mayor’s name to them. On July 2, 1829, Nicholas- painting by Pierre-Narcisse Guérin painting by Franz Xaver Winterhalter Gabriel was found dead, Charles X Louis-Philippe asphyxiated in an apart- ment in Paris. A note was left for Galois from his father, spring, Galois turned to the Bulletin de Ferussac to explaining that the ugliness left him no choice. publish three new short items. Ferussac and his group In January 1830, Cauchy finally did agree to report were the ones who had aided and employed Abel in to the Academy on Galois’ historic paper. However, 1826.10 Cauchy wrote, on January 18, that he was not well, and that he had to delay his report until the next week. The Revolutionary Activities following week Cauchy did show up; however, he made It was at this point, July 9, 1830, that King Charles a presentation on his own work, never mentioning X announced that he would solve his problems over the Galois or his manuscript. What happened that week to growing electoral success of his opposition. He would Cauchy, certainly, would make for a curious story; but simply rule by ordinance. His repressive ordinances on what is one to think of the other scientists at the Acad- July 25, 1830 were the immediate trigger for the July emy, staring at the naked emperor of the Hans Christian Revolution, whereby the republicans around Lafayette Andersen story? settled for an arrangement with Louis-Philippe, making After that performance, it had to be pretty clear that him the “Citizen-King.” Charles X abdicated in favor Galois might not be getting his two manuscripts back of his ten-year-old grandson and left for London. Galois any time soon. In February 1830, Galois rewrote his joined Lafayette’s National Guard—notably, the Artil- two papers into one submission for the Grand Prize in lery Unit section, the core of the republicans. Mathematics contest. That new paper went to the Acad- That same Fall, a fellow member of the Artillery emy’s permanent secretary, Joseph Fourier. We may Unit, the scientist François-Vincent Raspail, recruited presume that Cauchy got the paper from Fourier, since Galois evidently reported, to his close friend, Auguste Fourier died in May 1830 and the Galois paper was not found among the Chevalier, that Cauchy had seen this new paper. How- other papers in Fourier’s study. This is rather transparent, as no other ever, that paper also was lost, and consequently was submitted papers were similarly lost. 9 10. Shavin, see note 2. In 1831, the government would cancel the sub- eliminated from the Grand Prize determination. That scriptions of its various bureaus to Ferussac’s journal, causing financial hardship and loss of control over the journal. The journal died shortly 9. Blame for the lost paper is somehow associated with the fact that thereafter, following the Republic to the grave.

September 1, 2017 EIR Wake Up Call from Houston 53 Galois to his more militant re- What had Galois done at the publicans of the Society of famous May 9 celebration Friends of the People.11 In De- dinner, attended by two hundred cember, Louis-Philippe ordered or so republican enthusiasts, the disbanding of the Artillery many of them dressed in their Unit, the dismissal of Lafayette National Guard uniforms? After as head of the National Guard, the official (pre-arranged) toasts and the arrest of nineteen of its ended, more spontaneous toasts leaders. They were suspected of ensued. Etienne Arago, for ex- planning to turn over their heavy ample, received an enthusiastic artillery to “the people” and are response to his: “I drink to the charged with a conspiracy to Sun of 1831. May it be as warm overthrow the government. as that of 1830, but not blind us They were tried in April 1831. as the other did!” On March 13, 1831, finan- Amidst these sentiments, cier Casimir Périer replaced Galois put a point on matters. Pierre Laffitte as both President With one hand holding his wine of the Council of Ministers and glass and the other his meat Finance Minister. Typical of the knife, he calls out, “To Louis- machinations now afoot, the Philippe!” A ruckus ensued. government offered to confer Then he continues with words membership in the Legion of painting by Joseph-Désiré Court not well heard over the hubbub, Honor on Raspail, a noted scien- Gilbert du Motier, Marquis de Lafayette “. . . if he betrays his oaths.” Al- tist in his own right. He viewed exandre Dumas, in attendance, it as the bribe that it was, and signed his refusal “Ras- reported that, because of the presence of police agents, pail, plain citizen.” Périer made clear the government’s he “didn’t care to be compromised” and he “jumped game involving Raspail: “He must accept or else rot in from the window sill into the garden.” That night, the a dungeon!”12 The government’s actions from Decem- police agents at the dinner did indeed report Galois, and ber 1831 to April 1832—involving the dismissal of La- the next day he was arrested at his home and taken to fayette, the dismantling of the Artillery Unit of the Na- prison. tional Guard, the arrests of the Nineteen, the dumping of Laffitte for Périer—made it clear that the “Citizen- Prison and Auguste Chevalier King” was more the “Financier’s-King.” At his trial, on June 15, the judge probed Galois as On April 16, 1831, all nineteen republican leaders to why he was afraid the King would betray France. were found innocent, with great public celebration. Galois was, typically, simple and direct: “Everything Then on May 10, 1831, Galois was arrested for his role, encourages us to adopt this position . . . it is reasonable the previous evening, at a dinner party for the Nineteen. to believe that Louis-Philippe could betray the Nation. Of his last twelve months of life, Galois would spend He has not given us enough guarantees . . . [A]ll the ten of them imprisoned, most of them at Sainte-Pélagie King’s actions, though not yet showing his bad faith, prison. can lead us to doubt his good faith. One example is the background of intrigue to his accession to the throne.” 11. Raspail identified the goals of the “Friends of the People” in his At that point, he was prevented from going further, but January 1832 court case: “. . . an elected executive with a short term in office; a constitution, . . . universal military service without replace- it is a good bet that Périer’s name was about to enter the ment; juries chosen by lot from among all citizens; freedom of the press, analysis. Galois’ lawyer suggested to the judge that this assembly , and worship; the right to work; and the abolition of the death line of questioning may get into matters better left penalty.” See Dora B. Weiner’s Raspail: Scientist and Reformer, p. 171. alone, to which the prosecution quickly agreed. 12. Laffitte, much more the industrial banker, had been undermined by Périer throughout the first seven months of Louis-Philippe’s administra- Galois concluded, not as simply this time: “I con- tion. (Laffitte is named by Dumas as the source of Poe’s funds in Paris fess my behavior [with the toast] was rather sly. You in 1832.) can surely imagine the police inspector’s joy, when he

54 Wake Up Call from Houston EIR September 1, 2017 thought he had unmasked a con- of the National Guard. spirator . . . [However,] I cannot Some time in October, let what the public prosecutor during those three months of un- said, about it being impossible charged detention, Galois was for the King to be a traitor, go shown the rejection letter from unanswered. Nobody is foolish the Academy of Sciences, in- enough to believe now that a forming him that Poisson could king is perfect, especially since not understand Galois’ paper. when judges—who under (At least Galois’ fourth submis- Charles X, persecuted us, be- sion was not “misplaced” as cause we said that the King were the previous three—per- could neglect his duties—have haps one of the few accomplish- themselves now sworn alle- ments of the glorious events of giance to another man, who had 1830, the July Revolution and been placed on the throne, as the the flight of Cauchy!) Galois result of his predecessor’s stupid turned to Auguste Chevalier to behavior.” In one extended sen- privately publish his material. It tence, he managed to circum- was in one of these letters from vent his lawyer, the prosecutor prison that December that Galois and the judge. The jury ruled tells Auguste: “I must tell you that Galois was not guilty. François-Vincent Raspail how manuscripts go astray in the On the day of Galois’ trial, portfolios of the members of the his loyal friend, Auguste Chevalier, published in Le Institute, although I cannot in truth conceive of such Globe both praise of Galois’ mathematical genius and carelessness on the part of those who already have the condemnation of the unfair treatment directed toward death of Abel on their consciences.” It also raises the him. It related the story of the third lost paper, the one question, what could Auguste conceive when his cor- submitted for the Grand Prize sixteen months earlier. respondent was dead within six months? Galois added that in January 1831, he had rewritten that memoire and resubmitted it, but that Poisson at the Academy had sat on it. Three weeks after Chevalier’s V. Gisquet vs. the ‘Fierce publication, on July 4, 1831, Poisson reported to the Republican’ Academy that Galois’ paper was, as far as they under- stood, not worthy and was to be returned to Galois. Galois was arrested for the second and last time on Why Would Poe Pick on Gisquet? Bastille Day, July 14, 1831. This was to be the first Bas- Henri-Joseph Gisquet took over as the Prefect of tille Day since the July Revolution of 1830, and the Police on October 15, 1831, replacing Louis Sebastien police moved pre-emptively. During the night of July Saulnier, a man who lasted as prefect less than one 13/14, Republican leaders were arrested in their homes; month.13 (The eight prefects prior to Gisquet had aver- but Galois, perhaps as a precaution, was not at home. aged less than six months each.) Gisquet would serve On the 14th, in uniform, he led a group of 600 demonstrators. The police were waiting for Galois at a bridge, 13. It is quite possible that Gisquet’s appointment was conjoined with and he was arrested and jailed with, again, no violence Saulnier’s redeployment. That is, the royalist Saulnier seems to have earned his September 1831 appointment as Prefect, due to his sophisti- from the demonstrators. He was put back into the cal attack on the American government, claiming that a republic costs Sainte-Pélagie prison. There he joined his colleague, more to administer than a kingdom, published in the June 1831 Revue Raspail, who had been arrested and convicted the day Britannique (a journal that he had founded in 1825). LaFayette then after the May 9 celebration dinner. Evidently, Galois engaged James Fenimore Cooper to respond on the realities of govern- ing in America. In turn, Saulnier’s October 15 redeployment, taking was jailed for three more months before he was finally point against LaFayette, Cooper, and General Simon Bernard in a series charged—and the charge would be for bearing arms of public exchanges, became the infamous “Finances Controversy” in and wearing the uniform of the disbanded Artillery Unit France’s Chamber of Deputies.

September 1, 2017 EIR Wake Up Call from Houston 55 may have led to a renewed interest in Galois’ case, either for Poe’s 1841 “Murders in the Rue Morgue” or for Joseph Liouville’s 1843 decision to edit and publish Galois’ papers, or both. However, there is little doubt that it did provoke Gisquet, whose 1840 Memoires explained: “The government and the conspirators [Ras- pail’s Society of the Friends of the People] were engaged in a relentless daily struggle . . . I ordered the local branches dispersed as soon as they were founded, I had their papers confiscated, their members arrested.”14 In January 1832, the trial of Raspail and fourteen other leaders of the Society of the Friends of the People took place. Galois was a witness for the defense. The jury found them not guilty, but the judge gave Raspail fifteen months in prison for statements he made during the trial. Raspail had threatened the King for demand- ing “fourteen million for living expenses of an impov- erished France . . . .” Raspail’s attack reflected the then current debate in the Chamber of Deputies (January 16, 1832), known famously as the “Finances Controversy,” in which Lafayette addressed the cost of a kingdom versus that of a republic. Briefly, Saulnier’sRevue Bri- tannique, months earlier—the same Saulnier who had Prefect Henri Joseph Gisquet been Prefect of Police just prior to Gisquet—had claimed that the American republic cost its citizens for the next five years. Two weeks later, on October 29, more than the French kingdom (hence, France should a shot was fired into Galois’ room in prison, where all save money and choose a kingdom). This impelled La- three prisoners were quietly preparing for a night’s fayette to request James Fenimore Cooper, then living sleep. The shot was fired from a guard room. (It was in Paris, to provide Lafayette with an extensive report never determined whether this was just an accidental on America’s economy, government, and finances for discharge of a weapon, a deliberate attempt on Galois’ use in the debate.15 Cooper’s use of details of produc- life, or simply a warning shot, to send a message.) Galois tion and finances in the United States showed that a re- and the other two were imprisoned in the dungeon for public cost less per capita—basically because produc- complaining about being fired upon. The other prisoners tion per capita is higher.16 Importantly, General Simon revolted, and temporarily took over the prison, securing Galois’ release from the dungeon. Still alive, in Novem- 14. A typical police report under Gisquet: “To the Minister of the Inte- ber Galois was now officially charged by Gisquet for the rior, Sir: I have just learned that Raspail . . . has come to Lagny . . . and July 14 demonstration. Found guilty as charged, he was has participated in an anti government dinner party. Raspail’s apparent purpose is to learn about cereals and agriculture from peasants, farmers, scheduled for release on April 29, 1832. and millers. The information seems necessary for the book he is writing; Raspail described Galois in Sainte-Pélagie: “This but since the trip might conceal a political purpose, I thought it my duty slender, dignified child, whose brow is already creased, to keep you informed. Raspail will be discreetly watched during his after only three years’ study, with more than sixty years stay . . .” 15. Cooper’s November 1831 letter to Lafayette, “On the Expenditure of the most profound meditation; in the name of science of the United States of America,” used for Lafayette’s testimony to the and virtue, let him live! In two years’ time he will be Chamber of Deputies. Evariste Galois, the scientist! But the police do not 16. Lafayette had requested Cooper’s help in September 1831, but want scientists of this caliber and temperament to Cooper was finishing upThe Bravo, his novel on Venetian methods—a work completely appropriate both for 1831 Paris and for his American exist.” Raspail’s Reforme penitentiaire: Lettres sur les readers. After completing it, Cooper worked with Lafayette on the “Fi- prisons de Paris is the prime source for Galois’ time in nances Controversy” in November and December 1831. (Dumas’ claim jail. Years later, in 1839, his publication of those letters that Fenimore Cooper recommended Poe to him certainly dovetails with

56 Wake Up Call from Houston EIR September 1, 2017 Bernard, back from fourteen years in America, joined in the fray in coordination with Lafayette and Cooper. His relationship with West Point’s Sylvanus Thayer and with Poe is developed below.

The Death of Galois Galois’ prison sentence was completed on April 29, 1832. One month later, on May 29, he spends the night writing to friends, informing them of a duel the next morning, and to his most trusted friend, Auguste Chevalier, providing a quick summary of his mathematical work. (This letter gained fame for the claim that Galois invented group theory in the hours prior to his shooting.) On May 31, he dies in the Cochin Hospital, a hospital for the indigent. Evidently, he had been found the previous day in the coun- tryside by a peasant, with a bullet in his intes- tines. His brother, Alfred Galois, reported his last words were, “Don’t cry. I need all my cour- age to die at twenty.” It is not known what details Evariste Galois communicated to his younger brother that last morning in the hospital, but Alfred insisted from the very first that his brother’s death was the work of police agents. The next day, June 1, Galois’ associates at the Society of the Friends of the People plan the funeral and the political demonstration. Gisquet has advance notice, raids the meeting, and arrests thirty of the leaders.17 De- May 29, 1832: Galois’ last page, to Auguste Chevalier: “Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the spite all this, some two to three thousand show up importance of these theorems. Later there will be, I hope, some people for the funeral the next day and, despite Gisquet’s who will find it to their advantage to decipher all this mess.” insistence that they planned violence, they hold a funeral, not a violent demonstration. Galois occurs when he arrives in his Memoires at May The controversies over the shooting of Galois are 1831: “M. Galois, a fierce Republican, was killed in a well beyond the scope of this article. They involve, vari- duel by one of his friends.” Otherwise Gisquet’s ver- ously, police agents, a love interest, a duel with someone sion is that he had to raid the funeral planners because it possibly with the initials “L.D.,” and so on. The book- was really a plot to start a violent revolution. And de- length treatment by Einstein’s colleague, Leopold Infeld, spite Gisquet’s mass arrests, the only reason the 2-3,000 Whom the Gods Love, develops the role of the extensive attendees didn’t begin any trouble is because, at the last police-state control over the various characters. second, they heard that General Lamarque had just died What is of interest, rather, is what would have of cholera, and so decided to delay their revolutionary jumped out to Poe’s Dupin: Gisquet’s sole mention of rioting until Lamarque’s funeral, three days later. As Dupin concludes “The Murders in the Rue Morgue,” Poe’s 1831 request of Thayer for an introduction to Lafayette.) speaking of Police Prefect G____: “I like him espe- 17. Gisquet claims that he had put padlocks on the arranged meeting place, and that the group broke his padlocks. But, even if this were true, cially for one master stroke of cant, by which he has the point remains: Gisquet meant to physically prevent the meeting. He, attained his reputation for ingenuity. I mean the way he again, explains what isn’t and avoids what is. has ‘of denying what is, and explaining what isn’t.’ ”

September 1, 2017 EIR Wake Up Call from Houston 57 VI. Poe’s Dupin: Justice for Galois studied at West Point from July 1830 to March 1831, where the leading mathematics text, prepared by the Did Poe really have Evariste Galois in mind in cre- head of West Point’s Department of Engineering, was ating his singular C. Auguste Dupin figure? And, if so, Claudius Crozet’s 1821 A Treatise of Descriptive Ge- did he secure some justice for Galois? It is time now for ometry for the Use of Cadets of the U.S.M.A. Thayer a bit of Poe’s side of the story, overlapping the same had recruited Crozet from the Ecole Polytechnique period as Galois’ story. What was Poe’s competency in during his mission to Europe in 1815-1817, in prepara- “descriptive geometry” and what was his knowledge of tion for becoming superintendent of West Point Acad- Gisquet and Galois? emy in 1817. Thayer had spent most of his two years there in Thayer, the Ecole, Bernard and West Point Paris with members of the Ecole Polytechnique. It was In March 1831, Poe wrote to Sylvanus Thayer, the a difficult and repressive period, as the restoration of head of West Point, outlining his plan to go to Paris, and the monarchy included the castration of the Ecole. Both asking him to provide him with a letter of introduction Gaspard Monge and Lazare Carnot were forced out, to Lafayette and to Thayer’s contact(s) in Paris. Poe had and the Ecole was put under Cauchy’s control. Thayer

Poe’s letter to Gen. Sylvanus Thayer, March 1831: “Having no longer any ties which can bind me to my native country—no prospects—nor any friends—I intend by the first opportunity to proceed to Paris with the view of obtaining, thro’ the interest of the Marquis de Lafayette, an appointment (if possible) in the Polish Army. In the event of the interference of France in behalf of Poland this may easily be effected—at all events it will be my only feasible plan of procedure. The object of this letter is respectfully to request that you will give me such assistance as may lie in your power in furtherance of my views. A certificate of “standing” in my class is all that I have any right to expect. Any thing farther—a letter to a friend in Paris—or to the Mar- quis—would be a kindness which I should never forget.”

58 Wake Up Call from Houston EIR September 1, 2017 Fort Monroe, 1861 was led by Lafayette to former Ecole faculty, in particu- Colonel) Allan Magruder, remembered Poe as having lar, to his colleague, Gen. Simon Bernard, who, during “a wonderful aptitude for math . . . ,” only surpassed by 1816, would personally instruct Thayer in descriptive his poetry and his command of French. Even though geometry. Lafayette wrote President Madison that Gen- Poe had already decided to leave West Point, in the Jan- eral Bernard was the man to build fortifications for the uary 1831 math exam, he still placed 17th (out of 87 United States all along the East Coast.18 Bernard was cadets). Poe was not a slacker in the subject. appointed the head of the U.S. Corps of Engineers, and How much of Crozet’s Descriptive Geometry Poe the Chief of Fortifications. The first fort that Bernard was exposed to in his nine months there is unknown, built for the United States was Ft. Monroe, in the port of but his Dupin character certainly evidences a command Hampton and Norfolk, Virginia. Since Poe, prior to of the principles. Regardless, at the point of his ar- West Point, had been based there in 1829, he had the ranged early departure from West Point, Poe thinks his opportunity to study Bernard’s real-life application of best pathway is to pursue Thayer’s French contacts descriptive geometry. around Lafayette.20 It is also of note that Thayer’s friend and instructor, Gen. Bernard, decided, no later than Training at West Point February 1831, to return to post-Restoration France, to When, Poe arrived at West Point in June 1830, he become the head of the French Corps of Engineers. He promptly tested into the “first section,” which included arrived back in France in the Fall of 1831, and immedi- more advanced math topics (such as spherical ately joined in with Lafayette and Fenimore Cooper in geometry).19 A fellow West Point student (the future their defense of the United States in the national delib- erations over France’s future. Such a development is 18. Around 1816, Bernard was banished from Restoration France. He not one that a sharp fellow, such as Poe, would likely rejected an offer from Czar Alexander I, preferring to come to the have missed. United States. After the British navy had savaged the U.S. East Coast Alexandre Dumas tells the story that, in 1832, he during the War of 1812, Madison, learning the hard way, abandoned Jef- ferson’s pre-war, “penny-wise and pound-foolish” policy of not provid- and Poe investigated the murders in the Rue Morgue ing such logistical capability. (though with the actual French neighborhood, St-Roch, 19. In November 1830, Poe wrote home for math books, assumedly given). He followed up his story with another reference from his time at the University of Virginia. These included LaCroix’s to Poe’s visit with him, embedded in a manuscript not Elements of Algebra and Legendre’s Geometry. The Charlottesville pro- 21 fessor there who selected LaCroix for the students, one Charles Bon- written as fiction. This fits in perfectly with Poe’s neycastle, belonged—according to Cajori—“to that coterie of English mathematicians of which Herschel, Peacock, Whewell, and others were ville. members, and which introduced the Leibnizian notation . . . into Cam- 20. Coincidentally, Poe forces himself out of West Point at the exact bridge.” They wanted to bring LaCroix’s works into Cambridge Univer- same time that Galois is forced out of the Ecole normale—the end of sity. See discussion of John Herschel’s “The Principle of Pure Deism, in formal education for both of them. Opposition to the Dotage of the University” in The New Dark Ages Con- 21. Dumas’ version was published in his own Naples newspaper in spiracy by Carol White. Evidently, Bonneycastle did so for Charlottes- 1860-1861. A manuscript from 1864 surfaced in 1929, referencing

September 1, 2017 EIR Wake Up Call from Houston 59 intent, as expressed in his letter surge of republicanism in France to Thayer, and would account that would bring an end to the for his uncanny sense of a com- Restoration period. It is note- plicated political situation in worthy that Charles Dupin and France. However, putting aside Gen. Bernard were fellow min- the matter of Dumas’ story, there isters (of Navy and of War, is no doubt that over the next ten respectively) in the aborted No- years, Poe displayed a healthy vember 1834 French govern- interest, an amazing acumen, ment.24 It would, perhaps, have and a strategic overview of the been a semi-miracle if Dupin problems and developments in and Bernard had consolidated France—to a level that would power in 1834, but regardless, make it even more amazing had the attempt was the sort of de- he done all his work from Amer- velopment that would easily ica. A microcosm of this is en- have attracted Poe’s attention. veloped in the matter of Poe’s There is also good evidence name of the poet-mathemati- that Poe followed Charles Du- cian, “C. Auguste Dupin.” pin’s brother, André. He was the President of France’s Chamber The ‘Dupin’ Riddle Edgar Allan Poe of Deputies from 1832 to 1840. There is no one actual figure André had a reputation as the with the name “C. Auguste legal defender of oppressed re- Dupin” of whom Poe would have been aware. It is publicans during the Restoration period, most fa- somewhat ironic that the infighting that goes on over mously, of Marshal Ney. André attached himself to the issue is such a strong example of the nitpicking Louis-Philippe early on (1817) as the most sane pos- methods of Vidocq and Gisquet. Poe’s playfulness with sibility amongst the royal families. In 1830, upon the the name is a much richer story. The central figure for July Revolution, André initially became minister with- Poe is that of Charles Dupin, whose 1819 lecture on out portfolio in the first cabinet, that of Laffitte. André Monge’s Descriptive Geometry is excerpted above. Dupin himself was a subject of Lomenie’s Sketches of Dupin was Monge’s student at the Ecole Polytechnique,22 Conspicuous Living Characters of France, a work re- and his studies significantly overlap those of Crozet, viewed by Poe in the same April 1841 issue of Gra- Bernard, and Thayer. Dupin’s first major work, his 1813 ham’s Magazine in which C. Auguste Dupin first ap- Developpements de geometrie, was dedicated to peared. Monge. Recall that Poe, in his 1844 “Purloined Letter,” has Dupin also had a political career, which featured at- the narrator bring up two brothers, the minister who tempts to eliminate illiteracy and to educate skilled knows mathematics, and the brother, a man of letters labor in France, both for the purpose of enabling new and poetry. The narrator doubts that the minister whom scientific applications to radiate throughout produc- Dupin is tracking is really a poet-mathematician: tion.23 His electoral victory in 1827 was part of an up- “ ‘But is this really the poet?’ I asked. ‘There are two brothers, I know; and both have attained reputation in Poe’s visit, but not written as a tale. It states that James Fenimore Cooper provided Poe an introduction to Dumas. Most telling, 1832 is the only year of Poe’s writing career in which he sends nothing to a publisher. noted in particular the dirigist argument for uplifting the labor force. (The five stories published in 1832 were all given to his Philadelphia (Later, List’s 1841 work, The National System of Political Economy, publisher in 1831.) notes: “Men of the deepest insight into the condition of industry, such as 22. At the Ecole, Dupin constructed a specially designed structure for Chaptal and Charles Dupin, had expressed themselves on the results of the invasion of Great Britain, which he and his fellow students chris- this system in the most unequivocal manner.”) tened the Polytechnique. 24. The brawls over the cabinets of Louis-Philippe, the Citizen-King, 23. Dupin’s 1827 election pamphlet, Situation progressive des forces were complicated—but Lafayette’s 1830 deal with Louis-Philippe was de la France depuis 1814, was favorably noticed by Friedrich List and perhaps the high point of the republican influence. After December his Pennsylvania Society for the Encouragement of Manufactures. They 1830, most of the republican actions have a rear-guard quality.

60 Wake Up Call from Houston EIR September 1, 2017 letters. The Minister I believe has written learnedly on 1835 study of American economics, government, and the Differential Calculus. He is a mathematician, and society on behalf of the French government.26 How- no poet.’ ever, the best evidence that Poe had Galois in mind was “ ‘You are mistaken; I know him well; he is both. As provided by a fascinating clue that Poe left, one that poet and mathematician, he would reason well; as mere Dupin would have appreciated. mathematician, he could not have reasoned at all, and In 1846, a friend of Poe had brought up a current thus would have been at the mercy of the Prefect.’ ” legal controversy in France, involving two different Here, Poe seems to use the reality of the actual French translations of his “Murders in the Rue Morgue.” Dupin brothers to further his case for the poet-mathe- Poe corrects his friend’s assumption that the 1846 con- matician. But, even further, Prefect Gisquet can defeat tretemps was the first introduction of Poe’s name into either of the actual Dupin brothers should they be France. He cites examples of prior responses in France merely poet or mathematician—a fair description as to to his writings, beginning as follows: where the actual brothers might have fallen short, and a “The ‘Murders in the R. M.’ was spoken of in the pointed reminder as to why republicans need to hold Paris ‘Charivari,’ soon after the first issue of the tale in themselves to higher standards. Graham’s Mag: — April 1841.” The founder, publisher, and editor of Le Charivari How a Riddle Is Solved was one Charles Philipon, a political prisoner along So much for Charles and André Dupin. But Poe’s with Galois and Raspail at Sainte-Pélagie prison. Phili- Dupin is a “chevalier” named “C. Auguste Dupin.” pon’s four-page daily was noted for its political car- Certainly, the initial “C.” could certainly be a nod toons. It, along with its predecessor (named La Carica- toward Charles Dupin. However, no commentators ture), was at the center of attacks upon Louis-Philippe, deal with the obvious—the, as it were, “Purloined particularly because of his December 1830 betrayal of Letter”-type of clue of the remaining “Auguste” and France. For example, Philipon’s February 26, 1831 car- “chevalier.” There is an actual historical figure named toon, entitled “Foam of July,” had Louis-Philippe blow- Auguste Chevalier. We have met him. It is Galois’ most ing bubbles representing the promises of the July Revo- loyal friend, the one spending the 1830s making clean lution. Philipon was prosecuted (and acquitted) just copies of Galois’ manuscripts and trying to make prior to the trial of the nineteen republican leaders. He Galois’ mathematical breakthroughs known to Gauss, was next prosecuted in November 1831. Evidently, at Jacobi, and others. the trial itself, he presented his cartoon of “Louis- How would Poe have known about Auguste Cheva- Philippe as a pear,” which did the 1831 equivalent of lier? It was not until 1843, two years after Poe’s “Mur- “going viral.”27 ders in the Rue Morgue,” that Joseph Liouville went Poe, in simply invoking Le Charivari, speaks to public with the Galois papers, given to him by Cheva- anyone with ears what his introduction of Dupin is lier, in his announcement to the French Academy.25 Poe about. Clearly, Poe is aware of Philipon and his own might have read Galois’ last letter, the one to Auguste history with Gisquet, and he chooses to redirect any Chevalier, as it was published in the September 1832 discussion appropriately. issue of the Revue encyclopédique. Further, Poe might Various Poe experts assert, “Poe was simply mis- have discussed matters with Auguste’s close collabora- taken. We’ve examined issues of Le Charivari in the tor, his brother Michel Chevalier. Michel was in Balti- period after Poe’s work appeared, and we find nothing. more at the same time as Poe, during Michel’s 1833- Forget about it.” But it seems that Dupin has struck again. The “Poe experts”—perhaps better addressed as 25. Joseph Liouville, Professor of Analysis and Mechanics at the Ecole Polytechnique, was the hero of the Galois manuscripts. He received 26. Michel makes reference to Robert Walsh of Philadelphia’s National them in 1842, worked through them, and in 1843, announced to the Gazette as one of the two best editors in America, a man with whom Poe Academie: “These manuscripts have been entrusted to me by M. Au- had some dealings. Also, when Michel is in Baltimore, his reports refer guste Chevalier” and need to be published, something he accomplished to Laffitte, which might have been occasioned by discussions with Poe, in 1846. Liouville was a moderate republican and political collaborator but this is a pretty slender thread. of Arago (another attendee at the 1831 celebration of Lafayette’s Nine- 27. One unconfirmed story of Galois has him getting into trouble for a teen). “Louis-Philippe/pear” drawing on his jail cell wall.

September 1, 2017 EIR Wake Up Call from Houston 61 “Gisqueteers”—may search as relentlessly as Gisquet did in The Purloined Letter, for the words “Rue Morgue” in Le Charivari, but they will only explain what isn’t. But they deny what is. Poe’s readers are treated to a rare form of causal reasoning, but one open to any child encouraged to develop a healthy relationship with the imagination, one that strengthens the power of the creative reason. And for this alone, Galois, Gisquet’s “fierce republican,” may yet gain his full measure of justice.

VII. Poe’s Poet- Mathematician

Poe’s playful introduction to his Dupin character posed the mental work of working backwards, to retrace how the freely moving imagination traversed its course. In pursuing such concentrated work, one is not guaran- teed to capture the quarry every time—however it is an undeniably rich field, and the method indeed does work. In the spirit of Du- Philipon’s “Louis-Philippe as a Pear,” as it appeared in Le Charivari. pin’s method, which he described in reverse as: “The larger links of the chain run thus—Chantilly, kind of a god would have created something not in its Orion, Dr. Nicholas, Epicurus, Stereotomy, the street image? stones . . . ,” let us provide a brief example triggered not Have we learned from this rapid fire “scientific” in- by street stones, but by Galois’ work on the quintic. The vestigation that our God is a loving God, not a jealous reverse description runs as follows: “Immortality, one? Is this a beautiful idea, one that has the power to loving God, human, golden mean, dodecahedron, inspire—that is, one that may causally direct one’s play family of five, unlimited fantasies and unlimited space, towards loving future generations that we will never how to solve a fifth-power equation.” And now, let’s go see? Has our unique personality been damaged by this off to the races: “restriction” of our freedom, by having to deal with the Why would the solvability of equations involve de- problems of the world, into which we were created? Or scriptive geometry, and Platonic solids, in particular? does our mortal existence thereby touch immortality, How many regular solids are constructible in space? finding true meaning in our having been created? Oh, but aren’t they as unlimited as my possible fantasy It may be a struggle for the mind to traverse the uni- states? But why only five? What are the characteristics verse with any confidence in getting fruitful results, of this strange family of five? The dodecahedron is but it must be done, and it can be done. The power of somehow “more equal of the equals,” playing a gen- mind that Poe analyzes at some length (in, e.g., his erative role? What to make of its “golden mean” char- “Rationale of Verse”) is not fundamentally different acteristic? Have we now encountered a theological/ from that child, in the quiet evening hours, trying to cosmological principle—that is, why should the Cre- retrace how its own imaginative steps were taken. ator make man in the image of the Creator? Why Ideas take shape in the mind before they find their de- choose to produce a “subgroup,” that is, man, that lineation in words. somehow images the Creator? And, contrariwise, what Much is ventured about Galois, but in the “Gisquet”

62 Wake Up Call from Houston EIR September 1, 2017 fashion that Poe properly skewered. What is unmistak- acquires a feeling for the character of these families able about Galois, is that he clearly developed the “de- and individuals; it learns to see them combine them, scriptive geometry” to raise the mind’s analytic power. and foresee the results of their intersections and of their How is this different from what a true poet does? The more or less intimate contacts, etc. Thus the new geom- struggle involved is in so loving one’s fellow man, that etry greatly strengthens the imagination; it teaches you one takes into one’s heart—that one plunges into the how to grasp a vast collection of shapes quickly and history of man’s passions as reflected in the develop- precisely, to judge their similarities and differences and ment of language—both the noble passions and the de- their relations of size and position . . .” structive ones, and makes social a new pathway, one Hence, Evariste Galois, Poe’s poet-mathematician. with the increased power to conquer previous encrusta- tions of former progress. We used Charles Dupin’s quote on “descriptive ge- For Further Reading ometry” to characterize Galois’ method. Now, read it one last time, but with Poe’s command of poetry in Allen Salisbury, “Edgar Allan Poe: The Lost Soul of mind—where the “shapes of bodies in space” are now America,” Fidelio, Spring/Summer 2006, https://www. the “shapes of ideas in the mind (prior to verbaliza- schillerinstitute.org/fid_02-06/2006/061-2_Poe_Al- tion)”: len-S.html “One’s mind must be especially trained in this gen- Lyndon H. LaRouche, Jr., “The Day the Bomb Went eral geometry. One must be able to represent the shapes Off in Chicago: A Short Story,” The Campaigner, Vol. of bodies in space, and to ideally combine these shapes 14, No. 6, September 1981, http://www.wlym.com/ar- by the sole power of imagination. The mind learns to chive/campaigner/8109.pdf This article provides La- see inwardly and with perfect clarity the individual Rouche’s reflections on Poe and his “C. Auguste lines and surfaces, and families of lines and surfaces; it Dupin.” KNOW YOUR HISTORY! America’s Battle with Britain Continues Today The Civil War and the American System: How the Nation America’s Battle Was Won with Britain, America’s Untold 1860-1876 Story 1630-1754 by H. Graham Lowry W. Allen Salisbury, ed. $9.99 $15.00 PDF download PDF download

The Political Economy of the American Revolution Nancy Spannaus and Christopher White, Order online from eds. store.larouchepub.com $15.00 PDF download EIR News Service, Inc. P.O. Box 17390 Washington, D.C. 20041-0390 1-800-278-3135

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